/* 
 * jfdctint.c 
 * 
 * Copyright (C) 1991-1996, Thomas G. Lane. 
 * This file is part of the Independent JPEG Group's software. 
 * For conditions of distribution and use, see the accompanying README file. 
 * 
 * This file contains a slow-but-accurate integer implementation of the 
 * forward DCT (Discrete Cosine Transform). 
 * 
 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT 
 * on each column.  Direct algorithms are also available, but they are 
 * much more complex and seem not to be any faster when reduced to code. 
 * 
 * This implementation is based on an algorithm described in 
 *   C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT 
 *   Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics, 
 *   Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991. 
 * The primary algorithm described there uses 11 multiplies and 29 adds. 
 * We use their alternate method with 12 multiplies and 32 adds. 
 * The advantage of this method is that no data path contains more than one 
 * multiplication; this allows a very simple and accurate implementation in 
 * scaled fixed-point arithmetic, with a minimal number of shifts. 
 */ 
 
#define JPEG_INTERNALS 
#include "jinclude.h" 
#include "jpeglib.h" 
#include "jdct.h"		/* Private declarations for DCT subsystem */ 
 
#ifdef DCT_ISLOW_SUPPORTED 
 
 
/* 
 * This module is specialized to the case DCTSIZE = 8. 
 */ 
 
#if DCTSIZE != 8 
  Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ 
#endif 
 
 
/* 
 * The poop on this scaling stuff is as follows: 
 * 
 * Each 1-D DCT step produces outputs which are a factor of sqrt(N) 
 * larger than the true DCT outputs.  The final outputs are therefore 
 * a factor of N larger than desired; since N=8 this can be cured by 
 * a simple right shift at the end of the algorithm.  The advantage of 
 * this arrangement is that we save two multiplications per 1-D DCT, 
 * because the y0 and y4 outputs need not be divided by sqrt(N). 
 * In the IJG code, this factor of 8 is removed by the quantization step 
 * (in jcdctmgr.c), NOT in this module. 
 * 
 * We have to do addition and subtraction of the integer inputs, which 
 * is no problem, and multiplication by fractional constants, which is 
 * a problem to do in integer arithmetic.  We multiply all the constants 
 * by CONST_SCALE and convert them to integer constants (thus retaining 
 * CONST_BITS bits of precision in the constants).  After doing a 
 * multiplication we have to divide the product by CONST_SCALE, with proper 
 * rounding, to produce the correct output.  This division can be done 
 * cheaply as a right shift of CONST_BITS bits.  We postpone shifting 
 * as long as possible so that partial sums can be added together with 
 * full fractional precision. 
 * 
 * The outputs of the first pass are scaled up by PASS1_BITS bits so that 
 * they are represented to better-than-integral precision.  These outputs 
 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word 
 * with the recommended scaling.  (For 12-bit sample data, the intermediate 
 * array is INT32 anyway.) 
 * 
 * To avoid overflow of the 32-bit intermediate results in pass 2, we must 
 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26.  Error analysis 
 * shows that the values given below are the most effective. 
 */ 
 
#if BITS_IN_JSAMPLE == 8 
#define CONST_BITS  13 
#define PASS1_BITS  2 
#else 
#define CONST_BITS  13 
#define PASS1_BITS  1		/* lose a little precision to avoid overflow */ 
#endif 
 
/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus 
 * causing a lot of useless floating-point operations at run time. 
 * To get around this we use the following pre-calculated constants. 
 * If you change CONST_BITS you may want to add appropriate values. 
 * (With a reasonable C compiler, you can just rely on the FIX() macro...) 
 */ 
 
#if CONST_BITS == 13 
#define FIX_0_298631336  ((INT32)  2446)	/* FIX(0.298631336) */ 
#define FIX_0_390180644  ((INT32)  3196)	/* FIX(0.390180644) */ 
#define FIX_0_541196100  ((INT32)  4433)	/* FIX(0.541196100) */ 
#define FIX_0_765366865  ((INT32)  6270)	/* FIX(0.765366865) */ 
#define FIX_0_899976223  ((INT32)  7373)	/* FIX(0.899976223) */ 
#define FIX_1_175875602  ((INT32)  9633)	/* FIX(1.175875602) */ 
#define FIX_1_501321110  ((INT32)  12299)	/* FIX(1.501321110) */ 
#define FIX_1_847759065  ((INT32)  15137)	/* FIX(1.847759065) */ 
#define FIX_1_961570560  ((INT32)  16069)	/* FIX(1.961570560) */ 
#define FIX_2_053119869  ((INT32)  16819)	/* FIX(2.053119869) */ 
#define FIX_2_562915447  ((INT32)  20995)	/* FIX(2.562915447) */ 
#define FIX_3_072711026  ((INT32)  25172)	/* FIX(3.072711026) */ 
#else 
#define FIX_0_298631336  FIX(0.298631336) 
#define FIX_0_390180644  FIX(0.390180644) 
#define FIX_0_541196100  FIX(0.541196100) 
#define FIX_0_765366865  FIX(0.765366865) 
#define FIX_0_899976223  FIX(0.899976223) 
#define FIX_1_175875602  FIX(1.175875602) 
#define FIX_1_501321110  FIX(1.501321110) 
#define FIX_1_847759065  FIX(1.847759065) 
#define FIX_1_961570560  FIX(1.961570560) 
#define FIX_2_053119869  FIX(2.053119869) 
#define FIX_2_562915447  FIX(2.562915447) 
#define FIX_3_072711026  FIX(3.072711026) 
#endif 
 
 
/* Multiply an INT32 variable by an INT32 constant to yield an INT32 result. 
 * For 8-bit samples with the recommended scaling, all the variable 
 * and constant values involved are no more than 16 bits wide, so a 
 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply. 
 * For 12-bit samples, a full 32-bit multiplication will be needed. 
 */ 
 
#if BITS_IN_JSAMPLE == 8 
#define MULTIPLY(var,const)  MULTIPLY16C16(var,const) 
#else 
#define MULTIPLY(var,const)  ((var) * (const)) 
#endif 
 
 
/* 
 * Perform the forward DCT on one block of samples. 
 */ 
 
GLOBAL(void) 
jpeg_fdct_islow (DCTELEM * data) 
{ 
  INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 
  INT32 tmp10, tmp11, tmp12, tmp13; 
  INT32 z1, z2, z3, z4, z5; 
  DCTELEM *dataptr; 
  int ctr; 
  SHIFT_TEMPS 
 
  /* Pass 1: process rows. */ 
  /* Note results are scaled up by sqrt(8) compared to a true DCT; */ 
  /* furthermore, we scale the results by 2**PASS1_BITS. */ 
 
  dataptr = data; 
  for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { 
    tmp0 = dataptr[0] + dataptr[7]; 
    tmp7 = dataptr[0] - dataptr[7]; 
    tmp1 = dataptr[1] + dataptr[6]; 
    tmp6 = dataptr[1] - dataptr[6]; 
    tmp2 = dataptr[2] + dataptr[5]; 
    tmp5 = dataptr[2] - dataptr[5]; 
    tmp3 = dataptr[3] + dataptr[4]; 
    tmp4 = dataptr[3] - dataptr[4]; 
     
    /* Even part per LL&M figure 1 --- note that published figure is faulty; 
     * rotator "sqrt(2)*c1" should be "sqrt(2)*c6". 
     */ 
     
    tmp10 = tmp0 + tmp3; 
    tmp13 = tmp0 - tmp3; 
    tmp11 = tmp1 + tmp2; 
    tmp12 = tmp1 - tmp2; 
     
    dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS); 
    dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS); 
     
    z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); 
    dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), 
				   CONST_BITS-PASS1_BITS); 
    dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), 
				   CONST_BITS-PASS1_BITS); 
     
    /* Odd part per figure 8 --- note paper omits factor of sqrt(2). 
     * cK represents cos(K*pi/16). 
     * i0..i3 in the paper are tmp4..tmp7 here. 
     */ 
     
    z1 = tmp4 + tmp7; 
    z2 = tmp5 + tmp6; 
    z3 = tmp4 + tmp6; 
    z4 = tmp5 + tmp7; 
    z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ 
     
    tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ 
    tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ 
    tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ 
    tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ 
    z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ 
    z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ 
    z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ 
    z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ 
     
    z3 += z5; 
    z4 += z5; 
     
    dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS); 
    dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS); 
    dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS); 
    dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS); 
     
    dataptr += DCTSIZE;		/* advance pointer to next row */ 
  } 
 
  /* Pass 2: process columns. 
   * We remove the PASS1_BITS scaling, but leave the results scaled up 
   * by an overall factor of 8. 
   */ 
 
  dataptr = data; 
  for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { 
    tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7]; 
    tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7]; 
    tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6]; 
    tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6]; 
    tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5]; 
    tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5]; 
    tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4]; 
    tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4]; 
     
    /* Even part per LL&M figure 1 --- note that published figure is faulty; 
     * rotator "sqrt(2)*c1" should be "sqrt(2)*c6". 
     */ 
     
    tmp10 = tmp0 + tmp3; 
    tmp13 = tmp0 - tmp3; 
    tmp11 = tmp1 + tmp2; 
    tmp12 = tmp1 - tmp2; 
     
    dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS); 
    dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS); 
     
    z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); 
    dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), 
					   CONST_BITS+PASS1_BITS); 
    dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), 
					   CONST_BITS+PASS1_BITS); 
     
    /* Odd part per figure 8 --- note paper omits factor of sqrt(2). 
     * cK represents cos(K*pi/16). 
     * i0..i3 in the paper are tmp4..tmp7 here. 
     */ 
     
    z1 = tmp4 + tmp7; 
    z2 = tmp5 + tmp6; 
    z3 = tmp4 + tmp6; 
    z4 = tmp5 + tmp7; 
    z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ 
     
    tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ 
    tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ 
    tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ 
    tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ 
    z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ 
    z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ 
    z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ 
    z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ 
     
    z3 += z5; 
    z4 += z5; 
     
    dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, 
					   CONST_BITS+PASS1_BITS); 
    dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, 
					   CONST_BITS+PASS1_BITS); 
    dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, 
					   CONST_BITS+PASS1_BITS); 
    dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, 
					   CONST_BITS+PASS1_BITS); 
     
    dataptr++;			/* advance pointer to next column */ 
  } 
} 
 
#endif /* DCT_ISLOW_SUPPORTED */ 
